Uniform priors ?

We have no strong evidence for any particular prior and we therefore choose a simple factorized prior $p(\phi) = p(\theta)p(\nu_i)P(\tau_i)$. We assume a uniform prior on all trees $P(\tau_i) = 1/N_s$, we use a flat Dirichlet distribution prior for frequency parameters (i.e., all sets of frequencies are equally likely as long as they sum to one) and we choose a uniform positive prior for substitution rate parameters, gamma distribution parameter and branch lengths. Consequently, for all pairs of possible states $(\phi,\phi')$, the priors are equal. One should set upper limits in the case of uniform priors but since these parameters usually remain between reasonable limits during simulations these boundaries should not have any effect on experimental results unless unreasonable values are chosen. It is good practice to check whether these upper boudaries are reached while monitoring the parameters convergence.